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Volumn 76, Issue 12, 2006, Pages 1225-1237

On nonparametric maximum likelihood for a class of stochastic inverse problems

Author keywords

EM algorithm; Inverse problems; Longitudinal data; Maximum likelihood; Mixtures of probability measures; Nonlinear models; Repeated measurements data

Indexed keywords


EID: 33747892468     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2005.12.019     Document Type: Article
Times cited : (6)

References (38)
  • 1
    • 33747881154 scopus 로고    scopus 로고
    • Adams, R.A., 1975. Sobolev spaces, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York, London, Pure and Applied Mathematics, vol. 65, MR 56 #9247.
  • 2
    • 0002879516 scopus 로고    scopus 로고
    • Böhning, D., 1995. A review of reliable maximum likelihood algorithms for semiparametric mixture models. J. Statist. Plann. Inference 47, 1-2, 5-28, Statistical modelling (Leuven, 1993), MR 96h:62056.
  • 3
    • 33747892389 scopus 로고    scopus 로고
    • Böhning, D., 1999. Computer-assisted Analysis of Mixtures and Applications, Monographs on Statistics and Applied Probability, vol. 81, Chapman & Hall, CRC, Boca Raton, FL, Meta-analysis, disease mapping and others, MR 2001a:62001.
  • 4
    • 33747871702 scopus 로고    scopus 로고
    • Castillo, I., Loubes, J.-M., 2004. Estimation of the distribution of random shifts deformation. Prépublications de l'université d'Orsay.
  • 6
    • 33747888663 scopus 로고    scopus 로고
    • Chafai{dotless}̈, D., Concordet, D., 2005. On the strong consistency of approximated M-estimators. Preprint, http://hal.ccsd.cnrs.fr/ccsd-00005835 and http://fr.arxiv.org/abs/math.PR/0507102
  • 7
    • 33747874432 scopus 로고    scopus 로고
    • Chafai{dotless}̈, D., Dupuy, J.-F., 2005. Threshold censoring for stochastic inverse problems, in preparation.
  • 9
    • 33747877415 scopus 로고    scopus 로고
    • Concordet, D., Nunez, O., 2002. When is a nonlinear mixed-effects model identifiable? Preprint, http://www.biostat.envt.fr/
  • 10
    • 5444232913 scopus 로고    scopus 로고
    • Davidian, M., Giltinan, D., 2003. Nonlinear models for repeated measurement data: an overview and update. J. Agricultural, Biol. Environ. Statst. 8, 387-419 http://www4.stat.ncsu.edu/~davidian/.
  • 11
    • 0033243858 scopus 로고    scopus 로고
    • Convergence of a stochastic approximation version of the EM algorithm
    • MR MR1701103 (2001h:62031)
    • Delyon B., Lavielle M., and Moulines E. Convergence of a stochastic approximation version of the EM algorithm. Ann. Statist. 27 1 (1999) 94-128 MR MR1701103 (2001h:62031)
    • (1999) Ann. Statist. , vol.27 , Issue.1 , pp. 94-128
    • Delyon, B.1    Lavielle, M.2    Moulines, E.3
  • 12
    • 0002629270 scopus 로고
    • Maximum likelihood from incomplete data via the EM algorithm
    • with discussion, MR 58 #18858
    • Dempster A.P., Laird N.M., and Rubin D.B. Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. Ser. B 39 1 (1977) 1-38 with discussion, MR 58 #18858
    • (1977) J. Roy. Statist. Soc. Ser. B , vol.39 , Issue.1 , pp. 1-38
    • Dempster, A.P.1    Laird, N.M.2    Rubin, D.B.3
  • 13
    • 33747874689 scopus 로고    scopus 로고
    • Eggermont, P.P.B., LaRiccia, V.N., 2001. Maximum penalized likelihood estimation, vol. I. Springer Series in Statistics. Springer, New York, Density estimation, MR 2002j:62050.
  • 14
    • 0000073296 scopus 로고    scopus 로고
    • Rates of convergence for the maximum likelihood estimator in mixture models
    • (in English)
    • van de Geer S. Rates of convergence for the maximum likelihood estimator in mixture models. J. Nonparametric Statist. 6 4 (1996) 293-310 (in English)
    • (1996) J. Nonparametric Statist. , vol.6 , Issue.4 , pp. 293-310
    • van de Geer, S.1
  • 15
    • 33747884872 scopus 로고    scopus 로고
    • Ghosal, S., van der Vaart, A., 2003. Posterior convergence rates of Dirichlet mixtures of normal distributions for smooth densities, preprint.
  • 16
    • 33747880208 scopus 로고    scopus 로고
    • Gibaldi, M., Perrier, D., 1982. Pharmacokinetics, second ed., Dekker.
  • 17
    • 33747886296 scopus 로고    scopus 로고
    • Giutys, C., 1997. Adaptative density estimation in deconvolution. J. Am. Stat. Assoc.
  • 18
    • 33747892629 scopus 로고    scopus 로고
    • Groeneboom, P., Jongbloed, G., Wellner, J.A., 2002. The support reduction algorithm for computing nonparametric function estimates in mixture models, preprint.
  • 19
    • 0035470890 scopus 로고    scopus 로고
    • Consistent estimation of mixture complexity
    • MR MR1873331 (2002i:62064)
    • James L.F., Priebe C.E., and Marchette D.J. Consistent estimation of mixture complexity. Ann. Statist. 29 5 (2001) 1281-1296 MR MR1873331 (2002i:62064)
    • (2001) Ann. Statist. , vol.29 , Issue.5 , pp. 1281-1296
    • James, L.F.1    Priebe, C.E.2    Marchette, D.J.3
  • 20
    • 0000284439 scopus 로고
    • Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters
    • MR MR0086464 (19,189a)
    • Kiefer J., and Wolfowitz J. Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters. Ann. Math. Statist. 27 (1956) 887-906 MR MR0086464 (19,189a)
    • (1956) Ann. Math. Statist. , vol.27 , pp. 887-906
    • Kiefer, J.1    Wolfowitz, J.2
  • 21
    • 13444249563 scopus 로고    scopus 로고
    • Coupling a stochastic approximation version of EM with an MCMC procedure
    • (electronic), MR MR2085610 (2005c:62042)
    • Kuhn E., and Lavielle M. Coupling a stochastic approximation version of EM with an MCMC procedure. ESAIM Probab. Stat. 8 (2004) 115-131 (electronic), MR MR2085610 (2005c:62042)
    • (2004) ESAIM Probab. Stat. , vol.8 , pp. 115-131
    • Kuhn, E.1    Lavielle, M.2
  • 22
    • 3843063309 scopus 로고    scopus 로고
    • Nonparametric estimation in nonlinear mixed effects models
    • MR 2004b:62093
    • Lai T.L., and Shih M.-C. Nonparametric estimation in nonlinear mixed effects models. Biometrika 90 1 (2003) 1-13 MR 2004b:62093
    • (2003) Biometrika , vol.90 , Issue.1 , pp. 1-13
    • Lai, T.L.1    Shih, M.-C.2
  • 23
    • 0000525359 scopus 로고
    • The geometry of mixture likelihoods: a general theory
    • MR 85m:62008a
    • Lindsay B.G. The geometry of mixture likelihoods: a general theory. Ann. Statist. 11 1 (1983) 86-94 MR 85m:62008a
    • (1983) Ann. Statist. , vol.11 , Issue.1 , pp. 86-94
    • Lindsay, B.G.1
  • 24
    • 0000525358 scopus 로고
    • The geometry of mixture likelihoods II. The exponential family
    • MR 85m:62008b
    • Lindsay B.G. The geometry of mixture likelihoods II. The exponential family. Ann. Statist. 11 3 (1983) 783-792 MR 85m:62008b
    • (1983) Ann. Statist. , vol.11 , Issue.3 , pp. 783-792
    • Lindsay, B.G.1
  • 25
    • 33747887941 scopus 로고    scopus 로고
    • Lindsay, B.G., 1995. Mixture Models: Theory, Geometry, and Applications. Institute of Mathematical Statistics and the American Statistical Association.
  • 26
    • 0002661817 scopus 로고
    • A review of semiparametric mixture models
    • Statistical modelling (Leuven, 1993), MR 96h:62075
    • Lindsay B.G., and Lesperance M.L. A review of semiparametric mixture models. J. Statist. Plann. Inference 47 1-2 (1995) 29-39 Statistical modelling (Leuven, 1993), MR 96h:62075
    • (1995) J. Statist. Plann. Inference , vol.47 , Issue.1-2 , pp. 29-39
    • Lindsay, B.G.1    Lesperance, M.L.2
  • 28
    • 0023691625 scopus 로고
    • Nonparametric maximum likelihood estimation for population pharmacokinetics with application to cyclosporine
    • Mallet A., Mentré F., Steimer J.L., and Lokiec F. Nonparametric maximum likelihood estimation for population pharmacokinetics with application to cyclosporine. J. Pharmacokinet. Biopharm 16 3 (1988) 311-327
    • (1988) J. Pharmacokinet. Biopharm , vol.16 , Issue.3 , pp. 311-327
    • Mallet, A.1    Mentré, F.2    Steimer, J.L.3    Lokiec, F.4
  • 30
    • 0028301222 scopus 로고
    • Handling covariates in population pharmacokinetics
    • Mentré F., and Mallet A. Handling covariates in population pharmacokinetics. Int. J. Biomed. Comp. 36 (1994) 25-33
    • (1994) Int. J. Biomed. Comp. , vol.36 , pp. 25-33
    • Mentré, F.1    Mallet, A.2
  • 31
    • 0000963178 scopus 로고    scopus 로고
    • Optimal design in random-effects regression models
    • MR 1 467 058
    • Mentré F., Mallet A., and Baccar D. Optimal design in random-effects regression models. Biometrika 84 2 (1997) 429-442 MR 1 467 058
    • (1997) Biometrika , vol.84 , Issue.2 , pp. 429-442
    • Mentré, F.1    Mallet, A.2    Baccar, D.3
  • 32
    • 33747880097 scopus 로고    scopus 로고
    • Mesnil, F., 1999. Extension d'une méthode non paramétrique d'estimation dans des modèles mixtes pour l'analyse des données répétées. exemples en pharmacocinétique et en épidémiologie. Ph.D Thesis, University Paris XI, Faculté de médecine, Paris Sud.
  • 33
    • 84972545853 scopus 로고
    • A statistical perspective on ill-posed inverse problems (with discussion)
    • O'Sullivan F. A statistical perspective on ill-posed inverse problems (with discussion). Stat. Sci. 1 (1986) 502-527
    • (1986) Stat. Sci. , vol.1 , pp. 502-527
    • O'Sullivan, F.1
  • 34
    • 38249030045 scopus 로고
    • Consistency of maximum likelihood estimators for certain nonparametric families in particular: mixtures
    • MR 89g:62063
    • Pfanzagl J. Consistency of maximum likelihood estimators for certain nonparametric families in particular: mixtures. J. Statist. Plann. Inference 19 2 (1988) 137-158 MR 89g:62063
    • (1988) J. Statist. Plann. Inference , vol.19 , Issue.2 , pp. 137-158
    • Pfanzagl, J.1
  • 35
    • 38249030045 scopus 로고
    • Large deviation inequality for maximum likelihood estimators for certain nonparametric families in particular: mixtures
    • MR 89g:62063
    • Pfanzagl J. Large deviation inequality for maximum likelihood estimators for certain nonparametric families in particular: mixtures. Ann. Stats. 19 2 (1988) 137-158 MR 89g:62063
    • (1988) Ann. Stats. , vol.19 , Issue.2 , pp. 137-158
    • Pfanzagl, J.1
  • 36
    • 0034319191 scopus 로고    scopus 로고
    • Alternating kernel and mixture density estimates
    • MR MR1815573
    • Priebe C.E., and Marchette D.J. Alternating kernel and mixture density estimates. Comput. Statist. Data Anal. 35 1 (2000) 43-65 MR MR1815573
    • (2000) Comput. Statist. Data Anal. , vol.35 , Issue.1 , pp. 43-65
    • Priebe, C.E.1    Marchette, D.J.2
  • 37
    • 0000875518 scopus 로고    scopus 로고
    • Schumitzky, A., 1991. Nonparametric EM algorithms for estimating prior distributions. Appl. Math. Comput. 45(2), part II, 143-157, MR 92g:62047.
  • 38
    • 0000645875 scopus 로고
    • Large-sample inference for log-spline models
    • MR 91m:62073
    • Stone C. Large-sample inference for log-spline models. Ann. Statist. 18 2 (1990) 717-741 MR 91m:62073
    • (1990) Ann. Statist. , vol.18 , Issue.2 , pp. 717-741
    • Stone, C.1


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